Orthonormal Set

I have this problem that says show that is an orthonormal set relative to the inner product defined by . When I take the norms of each item in the set I get 1/2, 1, 1 respectively. Could someone point out to what I am doing wrong?

Are you sure it's supposed to be an orthonormal set and not just an orthogonal set? I get what you get for the norms, so the set is definitely not orthonormal w.r.t. that inner product. Maybe they meant to have the set